In french Québec when a family became so large in an area that multiple persons had the same christian & sur name, some would often take a "dit" name (which is to a surnanme somewhat like a "nick"name is to a christian name). e.g. Louis Pinard of LaRochelle, France and François Reiche of Languedoc, France; both settled in Trois-Rivièrs and Québec, PQ area; François married Louis' daughter; the Pinard family became large and the son who lived on the better road took that as a "dit" name (beau chemin) to distinguish himself from his brothers and cousins; but, François Reiche only had five sons (three died young, two became priests) and the name was about to die away;

Guillaume Beauchemin-dit-Pinard's son, Jean-Baptiste took his uncle François' name of "Reiche" as a dit name and styled himself, "Jean-Baptiste Reiche-dit-Beauchemin-et-Pinard",

when HIS grson moved to Nicolet, he shortened the pretentious surname to "Rêche"; which has been anglicized in the US as "Rash" and "Rashe", although some branches use "Raiche".

NOTE: MOST people of the "Rash" name (outside of New England) are NOT descended from French-Canadienne Raiche/Reiche family; but, immigrated from Europe directly to the southeastern United States.

NOTE: Those families who spell the name "Reiche" are equally as likely to be descended from Louis Pinard OR from Jean-Baptiste Reiche of Elzach, diocèse de Fribourg-en-Brisgau in the German Black Forest, Allemagne, [now] Germany.